## Finite-State Methods for Sub-Atomic Semantics## ESSLLI 2015, Barcelona (2nd week, Language & Computation)## Tim Fernando## AbstractSubatomic Semantics is according to Parsons 1990 "the study of those 'formulas of English' that are treated as atomic formulas in most logical investigations of English" including tense and aspect, and predication/modification. Implicit in the idea of subatomic semantics is non-atomicity, or put more positively, open-endedness. One form of open-endedness is variable adicity, the raison d'etre of events in Davidson 1967. A second form of open-endedness arises from the choice of temporal propositions, changes in which determine a notion of time. We analyze open-endedness uniformly through variations in bounded granularities shaping models within institutions in the sense of Goguen and Burstall 1992. Institutions are built around finite models of two kinds (i) strings, as in the Buechi-Elgot-Trakhtenbrot representation of regular languages in Monadic Second-Order Logic with successor, and (ii) deterministic automata, reduced under Myhill-Nerode to languages with transitions given by Brzozowski derivatives. The strings in (i) are used as timelines (approximating Priorean models), and the automata in (ii) as frames or records encoding a causal realm and/or linguistic resources. Central to Parsons' understanding of subatomic semantics is "the Panini-Ramsey-Davidson hypothesis that English sentences of the simplest sort contain some underlying reference to (quantification over) events or states." An addendum to the Panini-Ramsey-Davidson hypothesis is finite approximability: events are approximable at bounded granularities as runs of finite automata. The aim of the course is to show that these approximations are interesting, and that finite automata can, to a non-trivial extent, serve as the causal structures central, according to Steedman, to temporality in natural language. ## References- Robin Cooper & Jonathan Ginzburg, TTR for Natural Language Semantics, 2015
- Donald Davidson, The logical form of action sentences, 1967
- David Dowty, Word Meaning and Montague Grammar, 1979
- Kit Fine, Truthmaker semantics, 2015
- Joseph Goguen, Information integration in institutions, 2004
- Joseph Goguen & Rod Burstall, Institutions: Abstract model theory for specification & programming, 1992
- Hans Kamp & Uwe Reyle, From Discourse to Logic, 1993
- Leonid Libkin, Elements of Finite Model Theory, 2004
- Terence Parsons, Events in the Semantics of English: A Study in Subatomic Semantics, 1990
- Mark Steedman, The Productions of Time, 2005
- Andrzej Tarlecki, Rod Burstall & Joseph Goguen, Some fundamental algebraic tools for the semantics of computation: Part 3. indexed categories, 1991
## Lecture 1. Introduction: the Big Picture & an overview (slides)Prior and temporal sequences for natural language,Synthese, to appear (special issue on
Arthur Prior centenary)
Partitions representing change homogeneously, A
festschrift for Jeroen Groenendijk, Martin Stokhof & Frank Veltman,
2013 (pages 91--95)
Key phrases: McTaggart's dictum,
temporal proposition (fluent), homogeneity,
Dowty's Aspect hypothesis, segmentation, Dedekind cut
## Lecture 2. MSO/strings, compression & regular relations (slides)Constructing situations and time,J Philosophical
Logic 40: 371--396, 2011
Regular relations for temporal propositions, Natural
Language Engineering 17(2): 163--184, 2011
On regular languages over power sets, Journal of Language Modelling, to appear
(FSMNLP/IWPT 2013 special issue)
Key phrases: Carnap-Montague intensions,
Buechi-Elgot-Trakhtenbrot theorem,
Allen interval relations, Russell-Wiener-Kamp event structures,
finite-state transducers
## Lecture 3. A finite-state perspective on tense & aspect (slides)The semantics of tense and aspect: a finite-state perspective, In S. Lappin & C. Fox (eds.),
The Handbook of Contemporary Semantic Theory, Second Edition,
Wiley
Key phrases: telic, durative, Aktionsart,
imperfective, telic,
segmented, whole, incremental change, forces and inertia
## Lecture 4. Frames as finite automata (slides)Types from frames as finite automata, In Foret, Morrill, Muskens & Osswald (eds.), Preproceedings of the 20th Conference on Formal Grammar 2015, BarcelonaKey phrases: Leibniz' law,
Myhill-Nerode theorem, Brzozowski derivative,
Grothendieck construction, record types
## Lecture 5. Conclusion: partial views & prospects (slides)Two perspectives on change and institutions, In Joint Ontology Workshops proceedings (FOfAI), 2015, Buenos AiresKey phrases:
ontology, truthmakers, mereology,
institutions (logical pluralism, heterogeneity)
Last modified: 25 August 2015 |